1. Field of the Invention
The invention generally relates to baseball and, more particularly, to a statistical method for evaluating the performance of a relief pitcher.
2. Description of the Prior Art
Baseball thrives, and in large measure survives, by its ability to evaluate, differentiate and classify its product—namely, its players and teams. This is true for hitters, for pitchers, and, to a lesser extent, for position players in the field.
Who had the best season at the plate? Generally speaking, the batting average tells us.
Who had the most productive season? Perhaps it's the slugging percentage or the Runs Batted In (RBI) that tells us. Or is it the statistic that indicates which player crossed home plate the most times (Runs Scored)? Or perhaps the statistic that states who had the best on-base average, or the most walks, or the most hits.
Measuring pitching performance has also been one of the most common subjects of statistics, and can be found in newspapers from the 1800s. Which pitcher won how many games? The won/loss columns tell us. This is the most widely used measure of a pitcher's worth. Which pitcher struck out the most batters? Which pitcher yielded the fewest walks? Which pitcher allowed the fewest hits? Which pitcher allowed the fewest batters to cross home plate due to his mistakes (the Earned Run Average, or “ERA”)? This is the second most widely used measure of a pitcher's worth, after the total amount of “wins.” Which pitcher had the most “saves,” so to speak, out of the bullpen? A “save” is credited to a relief (or “substitute”) pitcher when the pitcher who starts the game is removed from the game while his team is in the lead; the relief pitcher holds the opposite team in check so that his team remains ahead and goes on to win the game. (It has been said that the “blown save” is baseball's most “deflating moment, and its most haunting,” The New York Times, Mar. 31, 2002, Sect. 8a, p. 3.)
The following is a more specific definition of a “save” in pitching: A pitcher can earn a save by completing all three of the following terms:                (1) Finishes the game won by his team;        (2) Does not receive the win;        (3) Meets one of the following three items:                    (a) Enters the game with a lead of no more than three runs and pitches at least one inning;            (b) Enters the game with the tying run either on base, at bat or on deck; and/or            (c) Pitches effectively for at least three innings.                        
The number of “saves” has been used for years as a measure of the value of a relief pitcher. Baseball is not immune to society's rush into specialization. Just as a general practitioner M.D. recommends a patient to a specialist, and an attorney might specialize in maritime law, baseball is becoming more and more specialized as to how it uses its players. Very few “complete”—nine-(or more)-inning games—are pitched by the starting pitchers. A manager will use a “pitch count” to determine how far his ace (the starting pitcher) can go. There are middle-inning (fifth–seventh inning) relief pitchers, and there are “closers,” who finish pitching the game.
Relief pitching has become an art and a specialty. However, the statistics related to relief pitching have not kept pace.
Assume the following situation. Several relief pitchers have come into a different number of games and have “inherited” a different number of base runners. However, all of these relief pitchers end the season with similar numbers of saves. Because the actual games each pitcher entered can be widely disparate, a fixed number of saves—say, 15—might not have the same value for each pitcher. It's possible that reliever no. 1 pitched in twice as many games as reliever no. 2. Clearly, in such a case, “15 saves” would not mean that they are of equal value. And what of the situations in which each of these pitchers allowed runs or scores and did not “save” the game (“blown saves”)?
Most of the baseball statistics we know are readily computed and reflect simple performance parameters. The common and not-so-common items used to measure pitching performance in the major leagues today include “Adjusted Pitching Runs” (“APR” or “PR/A”). This is an advanced pitching statistic used to measure the number of runs that a pitcher prevents from being scored compared to the League's average pitcher in a neutral park in the same amount of innings. This is similar to the “ERA” (“Earned Run Average”) and acts as a quantitative counterpart.
The abovementioned ERA is simply computed by the following formula:
  ERA  =      Rx9    I  where R=the number of earned runs and I=total no. of innings pitched.
The ERA is one of the oldest pitching statistics and is one of the most commonly used and understood statistics in the major leagues. Virtually every fan knows what it means, but many often forget the formula used to compute the pitcher's ERA.
The Earned Run Average Plus (“ERA+” or “RA”) is computed by dividing the league ERA by the ERA of a pitcher. This statistic uses a league-normalized ERA in the calculation and is intended to measure how well the pitcher prevented runs from being scoring relative to pitchers in the rest of the league. It is similar to the Hitters' PRO statistic.
Another commonly used statistic is the “Walks and Hits per Innings Pitched” (“WHIP”), which is computed as follows:
  WHIP  =            H      +      W        I  where H=number of hits, W=number of walks, and I=total number of innings pitched. There is a popular statistic that is probably used and frequently discussed in certain leagues. It was developed to measure the approximate number of walks and hits a pitcher allows in each inning he pitches, and then to compare the value received to other pitchers to formulate a pitcher's index.
The winning percentage is another common statistic in baseball and is also quite easy to understand and easy to compute. The primary purpose of this statistic is to gauge the percentage of a pitcher's games that are won.
In some instances, certain statistics become very sophisticated and more difficult to compute. Thus, for example, “Game Score” is computed as follows:
  GAMESCORE  =      50    +          3      ⁢      I        -          2      ⁢              (                  H          +          R          +          E                )              -    W    +    S    +          2              I        ′            where I=the number of innings pitched;    H=number of hits;    R=number of runs;    E=number of errors;    W=number of walks;    S=number of strikeouts; and    I′=the number of each full inning completed beyond the fourth inning.This advanced pitching statistic is used to measure how dominant a pitcher's performance is in each game he pitches. This statistic rewards dominance (strikes and lack of hits) while penalizing for walks.
As it clear from the above, the number of statistics that are followed by baseball enthusiasts is rather large. Some of these statistics are, of course, more important than others to either the fans or the ball clubs.
While some of the aforementioned pitching statistics reflect a pitcher's general performance, only some of the statistics reflect the additional pressures and expectations of pitchers during critical phases of the game, when the pitchers are under particular stress. As noted, the “Game Score” is a function of full innings completed beyond the fourth inning and, therefore, reflects the performance of the pitcher toward the second half of the game. Most of the pitching statistics do not, however, reflect other parameters that are inherently stressful to all pitchers and that all good relief pitchers must overcome, including the number of outs, the number of inherited runners and the specific bases where each inherited runner is located when the relief pitcher comes on. As suggested, the number of outs, the number of inherited runners and the specific bases on which they are located, as well as the specific inning in which the pitcher comes in can, separately and in combination, be particularly stressful to a pitcher. The ability of a pitcher to overcome such stressful conditions and provide a win has never been quantified. This problem has been recently discussed in “Top Relievers: Earning Saves by Putting Out Others' Fires” in The New York Times (Jun. 27, 2004) Section 8, page 10. Although this problem has been well defined, to date there has been no practical solution to it.